Example

Size an axial compressor for air service using the procedures outlined in the chapter. The following conditions are given:

Molecular weight: 28.65 Isentropic exponent: 1.395

Compressibility: 1.0

Inlet temperature: 80.0°F

Inlet pressure: 23.0 psia

Discharge pressure: 60.0 psia

Weight flow: 28,433.7 lb/min.

Step 1. Use Equation 2.5 to calculate the specific gas constant. R = 1.545/28.65 r = 53.93 specific gas constant Convert temperature to absolute.

Tj - 460 + 80 T| = 540°R k/(k - 1) = 1.395/.395 ky(k~ 1) = 3.53 (k- l)/k = .395/1.395 (k 1 )/k = .283

Step 2. Substitute into Equation 2.10 and, using the conversion constant of 144 in2/ft2, calculate the inlet volume.

LP x 53.93 x 540 V1 23x144

Q, = 250,000 cfm inlet flow

Select the frame size (hub diameter, dh) using Figure 6-9. At the inlet vol ume value, a 44 frame is selected with a maximum speed of 3,150 rpm. This frame has a 44-inch hub diameter.

Step 3. To calculate the number of stages, the overall head is required. The head is calculated using Equation 2.70 and rp = 60/23 = 2.61 for the pressure ratio.

Ha = 32,080.2 ft-lb/lb total adiabatic head

Then using Equation 6.12 and the pressure coefficient, p = .29 and um -720 fps given in the chapter.

This value is rounded to the next whole number, 7. Recalculate p. using Equation 6.13 and the number of stages.

Since the p, is within 5% of the target value of .29, then use the mean blade velocity, um = 720 fps, as a final value and proceed with the sizing.

Step 4. Calculate the tip diameter using Equation 6.17.

d, = 63.53 in. first stage tip diameter

Check the hub-to-tip ratio, dh/dt. If greater than .67, continue. If not, go back to Step 2 and try another frame size.

This is greater than the stated limit, proceed to the next step.

Step 5. Calculate a mean diameter in preparation for calculating the compressor speed. Use Equation 6.18.

dm = 53.77 in. mean blade diameter

Calculate the speed using Equation 6.18.

N = 3066 rpm compressor speed

The speed just calculated is less than the maximum speed of 3150 given for the frame and is therefore acceptable.

Step 6. Calculate the last stage volume using Equation 6.20.

Qis = 138,698.9 cfm last stage volume

Using Equation 6.14 calculate the last stage tip diameter.

d, = 50.9 in. last stage tip diameter

Check the last stage hub-to-tip ratio. It should be less than 0.9. If a problem is encountered with meeting this ratio, select another frame. If one frame exceeds the lower limit and the alternative choice exceeds the higher limit, multiple cases may be needed. The casing passing the lower hub-to-tip limit of .67 should be selected, except with the pressure ratio varied until the high limit of .9 can be met. The balance of the compression could be completed with a centrifugal compressor. In sizing a centrifugal compressor by the procedure outlined in Chapter 5, the speed of the axial can be assumed to be the centrifugal speed. This would permit a tandem drive arrangement. Cooling can be added, depending on the discharge temperature of the axial. Calculate the last stage hub-to-tip ratio.

This value is less than the limit of 0.9. Proceed to the next step.

Step 7. Calculate the discharge temperature using the efficiency stated of .85 and Equation 4.6.

t2 = 278.2°F discharge temperature

Step 8. Calculate the shaft horsepower using Equation 4.7 and the mechanical losses from Figure 6-9 at the frame selection. Use the efficiency Ha - -85 as recommended.

33,000 x.85

W? = 32,589hp shaftpower

Application Notes

The axial compressor is a highly refined, sophisticated compressor. It is capable of very high efficiency, to the point that some of the designers feel there is no area of improvement left. As efficiency gets higher, the margin left between the ideal and current design makes each point much more difficult to achieve. Most of the development activity has centered on higher velocities, and the development of cascade data at the higher Mach numbers. The developments are more significant in aircraft engines where power-to-weight (size) ratio has a greater impact. The technology, however, is being applied to the land-based axial compressor. While the cost of the machine will somewhat follow the number of stages, and cost is probably one of the more significant factors retarding the application growth. The higher Mach number stages are more expen sive to manufacture, somewhat offsetting the savings of having fewer stages. Gas turbines seem to be using the newer technologies as their size capabilities are increased.

Because the axial is a sophisticated compressor, it tends to show its "blueblood" at times, in lack of ability to cope with common plant problems such as fouling. The sophisticated airfoils, while capable of such nice high efficiency performance, have a real problem with dirt. It does not have to be polymers or other chemical reactions of the kind that cause problems with the centrifugal, but rather it can be ordinary atmospheric air. Some of the tendency to foul can be averted by changing the reaction at the expense of efficiency. This has not been completely successful, however, due to the complex modes in which fouling takes place. The best solution is filtration, which is attended by an increase in inlet pressure drop. The filtration should be of the dry type. Moisture, even a high humidity, can make whatever dirt does pass through the filter stick to the blading. On-stream washing has been successful in some cases, but must be carefully done and is somewhat of a trial-and-error method, until an operable mode is established. An alternative to washing is the use of organic abrasives. These have been reported as an effective and low-cost method of cleaning up this type of build-up [2j.

Larger axial compressors have a physical space problem with the inlet nozzle, requiring a departure from the conventional round flanged nozzle customarily used in centrifugal application. This means either custom engineered rectangular duct work supplied by the user or an off-machine transition piece. For atmospheric suction compressors, where the inlet is connected to a nearby filter housing, this is not a serious problem.

Inlet startup screens have been recommended for other compressors covered in the earlier chapters. If the point has not been made yet, it should be with the axial compressors. Considering that most of the cost of the compressor is in the hundreds of vulnerable blades just waiting to be hit by some foreign object, it should be obvious that some protection is needed until the piping has been proven to be clear and clean.

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